Mathematica Programming language provides fully integrated environment for the technical computing. Mathematica has become standard in a great many organizations, and it is used today in all the Fortune 500 companies, all of the 15 major departments of USA government. Mathematica use heavily on a daily basis and very frequently need the full power it can give, in terms of speed, numerical and symbolic capabilities. Mathematica seems to be an ideal tool for development of toy - models, prototypes, or just ideas. While Mathematica may be also quite useful for validating some ideas or solutions, as well as to power some quite complex technologies also in their final form, my feeling is that it may be most useful as a tool of experimental research (or programming), where the answer (or design) is not known in advance.
Plot[{ArcTan[x],ArcTan'[x]},{x,-10,10}, PlotStyle->{RGBColor[0,0,1],RGBColor[1,0,0]}];
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